When \(H\)  is one dimensional, without loss of generality (see [1]}), we consider the following splitting
\(H:=\lbrace  (x_1,0\dots , 0)\,:\, x_1 \in \mathbb {R}\rbrace , \qquad N:=\lbrace  (0,x_2,\dots , x_{m+n})\,:\, x_i \in \mathbb {R}\rbrace .\) 
